Experimental Simulation of In Situ Axial Loading on Deep High-Pressure Frozen Ice

Abstract

The mechanical properties of high-pressure frozen ice are critical design parameters for deep artificial ground freezing and ice sheet drilling operations, making their investigation fundamentally significant. In this study, ice specimens were prepared at −10 °C under freezing pressures of 10, 20, 30, 40, and 50 MPa. In situ axial loading simulation experiments were conducted to investigate their mechanical behavior and macroscopic deformation characteristics during failure. The experimental results indicate that the deviatoric stress–axial strain curves of the ice specimens exhibited a rapid yet smooth transition before and after reaching the peak deviatoric stress, with all samples exhibiting ductile failure. The peak deviatoric stress initially increased and then decreased with increasing freezing pressure, reaching a maximum value of 8.61 MPa at a critical transition pressure of 20 MPa, eventually declining to a minimum of 1.66 MPa at 50 MPa. The residual deviatoric stress decreased significantly with increasing freezing pressure, declining from approximately 3.5 MPa at 10 MPa to 0.85 MPa at 50 MPa. The peak tangent modulus demonstrated a fluctuating trend with increasing freezing pressure, ranging from 1.76 to 2.37 GPa. As the freezing pressure increased, the failed ice specimens transitioned from a densely cross-cracked state to a highly transparent phase, and finally to a sparsely cross-cracked morphology.

1. Introduction

The capabilities for vertical shaft construction in deep strata and drilling through thick ice sheets holds significant research value for resource extraction, biological exploration, and investigation of Earth’s evolution [1,2,3]. Currently, the depth of deep vertical shaft construction has exceeded 1000 m [4]. As an essential auxiliary technique, artificial ground freezing (AGF) effectively enhances the strength of surrounding rocks and soils while providing critical waterproofing [5,6,7]. However, as shaft depth increases, field monitoring data indicate that current design systems still rely on theories developed for shallow conditions, resulting in excessively large designed thicknesses of frozen walls, which is primarily due to an insufficient understanding of the mechanical properties of deep-frozen rocks and soils [8,9]. The pore-ice is an important influencing factor on the mechanical properties of deep-frozen rock and soil mass. Meanwhile, basal ice in certain polar ice sheets, particularly in subglacial lakes bottom, forms through water freezing under high pressure [10,11]. With increasing depth, drilling operations frequently encounter abrupt changes in ice properties, such as brittle ice zones, leading to challenges in drilling and ice core extraction. Therefore, the research on the mechanical properties of deep high-pressure frozen ice is the basis for the rational design of freezing walls in deep AGF engineering and technological innovation in polar ice sheet drilling operations.

As a fundamental component of frozen geomaterials, ice governs their mechanical properties and is a critical determinant of the bearing capacity of frozen soil-rock masses [12,13]. However, unlike conventional non-pressure frozen ice [14], the ice formed within frozen geomaterials during deep shaft construction using AGF develops under high pore-water pressure conditions [15,16]. This type of ice is herein referred to as high-pressure frozen ice (HPFI). Currently, the maximum recorded depth for ground freezing is 755 m in soil strata and 990 m in rock strata, with ongoing efforts pushing towards 1000 m mark. In water-rich strata at depths of 1000 m, the freezing pressure, accounting for ice-expansion-induced local stress concentrations, can exceed 10 MPa [17], and it increases further with greater shaft sinking depths. This results in the ice bodies in the rock and soil voids being frozen by high-pressure water during deep AGF process. Beyond deep AGF projects, HPFI is also widely present in nature. The polar regions are endowed with abundant natural resources, including marine and biodiversity resources, as well as genetic materials, which hold significant value for exploration. Massive polar ice sheets [2,11] and the basal ice of subglacial lakes [10] form through the freezing of water under high pressure. At present, drilling remains the most direct and effective technical method for deep ice core retrieval and subglacial environment investigation in these areas, and its application is subject to significant influence from the mechanical properties of ice. Polar drilling operations routinely reach depths exceeding 3000 m and are progressing toward the 4000 m mark [18,19]. Drilling results of polar ice sheets indicate the existence of a “brittle ice zone” at depths ranging from approximately 400 to 1300 m below the ice surface, where drilling and core extraction face numerous challenges [20,21,22]. Specifically, high-pressure frozen phenomena also exist in water-bearing celestial bodies in space. For example, Europa, one of Jupiter’s moons, has a liquid water layer encased in an ice shell that may be up to 150 km thick [23]. At the base of this ice shell, continuous phase changes in high-pressure water give rise to unique frozen ice structures. Precise observations of the deformation characteristics of the ice shell have become a key breakthrough in detecting the distribution of liquid water resources in outer space. Overall, researching and revealing the mechanical properties of HPFI are of great importance for deep artificial ground freezing, polar scientific expeditions, and outer space exploration.

In recent years, researchers worldwide have conducted extensive experimental studies on the mechanical properties of frozen ice [24,25], yielding significant findings. For instance, Dong et al. conducted axial compressive and flexural strength tests on river ice under varying temperatures and loading rates [26]. The results demonstrated that river ice exhibits ductile failure at low loading rates and brittle failure at high loading rates, with identifiable brittle-ductile transition points. Both axial compressive and bending strengths were found to be temperature-sensitive, increasing as the temperatures decreased; however, the mechanical properties degraded when temperatures dropped below −30 °C. Dutta et al. employed a split Hopkinson pressure bar to investigate the dynamic strength characteristics of columnar ice at very high strain rates (10–15 s⁻¹) [27]. Their findings revealed that the strength values exhibited negligible variation within this strain rate range, and, regardless of the loading rate, the failure strain of ice consistently remained approximately 0.1%. Gharamti et al. conducted creep/cyclic-recovery and monotonic ramp tests on freshwater ice specimens to study their time-dependent behavior [28]. The results indicated that creep and cyclic loading sequences did not significantly influence the failure load or crack opening displacements at crack initiation, with the ice exhibiting elastic-viscoplastic behavior under the tested conditions. The loading phases exhibited an immediate transition from transient to steady-state creep, resulting in permanent displacement. Farid et al. conducted triaxial experiments on atmospheric ice samples collected from ice accumulated on a rotating cylinder inside the INGIVRE icing wind tunnel under various conditions [29]. It was found that near the melting point, the strength of atmospheric ice initially increased with confining pressure up to a certain limit, after which it dropped significantly. At lower temperatures, strength increased continuously with confinement, the Mohr-Coulomb and Hoek-Brown failure criteria were evaluated and found to be applicable for predicting atmospheric ice failure. Overall, current research on ice mechanics is relatively extensive. However, the ice samples used in these experiments are either prepared under pressure-free conditions or sourced from shallow natural ice. With the continuous exploration of polar ice sheets and the increasing depth of artificial ground freezing projects, existing findings on pressure-free ice are insufficient to effectively support engineering applications and related scientific explorations. In order to explore the mechanical characteristics of deep HPFI, Yang and Wang developed an infinite stiffness freezing triaxial experimental system [30], which realizes sample preparation and mechanical testing in the same pressure chamber. On the basis of this experimental system, Wang et al. investigated the effect of freezing pressure on the uniaxial compressive strength of ice samples and provided a detailed demonstration of the reliability of the experimental system and the precision of ice-sample preparation [30,31]. Subsequently, Sun et al. conducted triaxial compression experiments, focusing on the influence of the axial loading rate on the shear strength of ice specimens and introduced cellular automata simulation methods for the analysis of the mechanical properties of HPFI [32,33]. However, there is still a lack of triaxial experimental research on HPFI under the specific stress path of in situ loading or unloading, particularly under high freezing pressures.

In this study, high-pressure frozen ice specimens were prepared using the KTL-401 Virtual Infinite Stiffness Triaxial Testing System, originally developed by Yang and Wang, under conditions of −10 °C and confining pressures of 10, 20, 30, 40, and 50 MPa. To simulate the in situ stress path under axial loading, the experiments consistently maintained the confining pressure on the ice specimens equal to the freezing pressure, followed by axial loading until deformation and failure occurred. The evolution of the mechanical parameters with freezing pressure was then thoroughly analyzed, with particular focus on the characteristics of the deviatoric stress–axial strain curves, the peak deviatoric stress, residual deviatoric stress, tangent modulus, and macroscopic deformation.

2. Materials and Methods

2.1. Experimental Instruments

The KTL-401 Virtual Infinite Stiffness Triaxial Testing System was employed for the preparation and mechanical testing of HPFI, as shown in Figure 1. This experimental system enables the preparation of ice samples and subsequent mechanical testing to be conducted within the same triaxial pressure chamber, effectively eliminating errors associated with temperature and stress fluctuations caused by sample transfer in conventional ex situ preparation and testing methods. The mechanical field control system mainly included a stiff loading frame and a volumetric pressure controller, capable of applying axial loads up to 400 kN and confining pressures up to 64 MPa, with accuracies of 0.01% and 0.1%, respectively. The temperature field control system consists of three cryogenic channels integrated at the top, side, and bottom of the triaxial pressure chamber, each independently connected to a refrigerated bath chamber. This configuration enables the precise regulation of the temperature field within the pressure chamber, allowing accurate control over the initial position, propagation direction, and freezing rate of the freezing front. The refrigerated bath chamber can achieve a minimum temperature of −40 °C with a temperature control accuracy of 0.1 °C.

2.2. Manufacturing Method for Cylindrical Pressure-Frozen Rce

The flexible water sample undergoes controlled axial freezing within the system, where its expansion is directionally constrained under high pressure to form standardized cylindrical ice specimens. Because the experimental system requires an ice specimen with dimensions of Φ 61.8 mm × 125 mm, a water sample measuring Φ 61.8 mm × 114.7 mm is prepared based on the fact that the volume of Ih-type ice expands by approximately 9% compared to water. The schematic diagram of water sample preparation and installation is shown in Figure 2. The distilled water sample is filled into a cylindrical heat-shrink tube formed by an assembled rigid structure mold and is installed into the system without deformation using a specially designed suspension frame. After water-sample installation, No. 10 aviation hydraulic oil is injected into the pressure chamber as the confining medium, and the confining pressure is gradually increased to the target freezing pressure under constant axial displacement conditions. The system then switches to pressure-stabilization mode, wherein the pressure-volume controller maintains a constant volume of the confining medium while the axial loading frame operates in constant-pressure servo mode, thereby allowing the freeze-induced expansion force to be released axially to form a standardized cylindrical ice specimen. A detailed discussion of the experimental instrumentation and sample preparation accuracy is provided in Reference [32].

2.3. Experimental Scheme

To investigate the influence of different freezing pressures on the mechanical properties of HPFI under in situ axial loading, ice samples were prepared under freezing pressures of 10, 20, 30, 40, and 50 MPa, respectively. Experiments under each operating condition were repeated three times to mitigate random experimental errors. During the ice-sample preparation process, both the axial and confining pressures were maintained equal to the freezing pressure. Subsequently, the confining pressure was held constant while axial pressure was applied at a constant strain rate. In accordance with engineering practice and conventional ice testing standards, the strain loading rate was set to 1.5 × 10⁻⁵ s⁻¹. The test temperature was maintained at −10 °C, a temperature commonly adopted in international laboratory investigations of ice mechanics. The detailed experimental scheme and corresponding parameters are systematically summarized in

Table 1. A summary of the experimental scheme.

Case	Freezing Pressure (MPa)	Test Temperature (°C)	Strain Loading Rate (s−1)
1	10	−10	1.5 × 10−5
2	20
3	30
4	40
5	50

.

3. Results and Discussion

3.1. Deviatoric Stress–Axial Strain Curves

Under identical conditions, the consistent evolutionary trend observed in the deviatoric stress–axial strain curves of ice specimens prompted the extraction of a representative curve from the raw datasets to clearly illustrate the influence of freezing pressure under axial loading, as shown in Figure 3. By increasing the axial strain, the deviator stress rapidly rises to a peak value, then begins to decline and gradually transitions to a steady state. Notably, the deviatoric stress–axial strain curves for ice specimens formed at different freezing pressures exhibit a rapid yet smooth transition before and after reaching the peak deviatoric stress, with no observable yield plateau or rapid stress drop, which exhibit characteristics of ductile failure. The curves under different freezing pressures exhibit distinct peak strengths but have nearly identical overall trends, and consistently display four characteristic stages: elastic deformation, yielding, softening, and residual.

In this study, after excluding the initial adjustment phase, the elastic deformation primarily occurred within the 0–1% strain range. During the elastic deformation stage, the internal structure of the ice remains largely intact, and the deviatoric stress increases linearly with axial strain. As axial loading continues, the ice enters the yielding stage, during which the slope of the deviatoric stress–axial strain curve gradually decreases, marking the onset of nonlinear deformation, while the load-bearing capacity of the ice continues to increase. Upon reaching the peak stress, the ice attains its maximum load-bearing capacity, indicating that the overall structure is approaching failure. Subsequently, a rapid decline in stress occurs, marking the post-peak softening stage, during which the load-bearing capacity of the material deteriorates sharply. By the time the strain reached 5%, all specimens entered the residual stage characterized by relatively stable stress levels, demonstrating ductile failure behavior.

3.2. Peak Deviatoric Stress

Figure 4 presents the evolution of peak deviator stress and corresponding axial strain with freezing pressure for HPFI under axial loading. The influence of freezing pressure on peak deviatoric stress exhibits distinct nonlinear characteristics, with an initial increase followed by a decrease. At the freezing pressure of 10 MPa, the peak deviatoric stress reached 7.65 MPa. The transition point occurred at the freezing pressure of 20 MPa, where the peak deviatoric stress attained the maximum value of 8.61 MPa, marking the critical threshold between increasing and decreasing trends. With further increases to 30, 40, and 50 MPa, the peak deviatoric stress progressively decreased to 6.99 MPa (an 18.9% reduction from the peak), 5.52 MPa (a 35.9% reduction), and 1.66 MPa (a 80.7% reduction). The most significant strength degradation (a 69.9% reduction) occurred between 40 and 50 MPa.

The axial strain corresponding to the peak deviatoric stress primarily ranges between 0.24% and 0.93%, all of which are below 1%. Under freezing pressures ranging from 10 MPa to 30 MPa, the average value of this strain fluctuates within a narrow range, with a maximum variation in merely 0.1%. As the freezing pressure increases, the corresponding average value decreases significantly. Compared to 0.78% at 30 MPa, it drops to 0.55% and 0.32% at 40 MPa and 50 MPa, respectively. However, this does not necessarily imply that higher freezing pressure directly reduces the deformation compatibility of the ice mass. Because this study simulated the in situ axial loading of deep HPFI, the confining pressure experienced during the axial loading process also gradually increased with freezing pressure. Therefore, the observed axial strain evolution corresponding to the peak deviatoric stress resulted from the combined action of freezing pressure and confining pressure.

Additionally, the average axial stress corresponding to the peak deviatoric stress demonstrated a highly significant, approximately linear positive dependence on freezing pressure, as evidenced by a near-unity linear regression coefficient (R²) of 0.99, with the corresponding fitting equation provided in Figure 5. More specifically, the axial stress exhibited a substantial escalation from approximately 17.65 MPa under a freezing pressure of 10 MPa to roughly 51.66 MPa when the freezing pressure was elevated to 50 MPa, underscoring a pronounced strengthening effect in response to freezing and confining conditions.

3.3. Residual Deviatoric Stress

A comparative analysis of the deviatoric stress–axial strain curves in Figure 3 indicates that the stress levels of the ice specimens stabilized at approximately 5% axial strain. Therefore, the deviatoric stress at this point is defined as the residual deviatoric stress. The corresponding values under different freezing pressures are presented in Figure 6, exhibiting an overall decreasing trend with increasing freezing pressure. The ice specimen under 10 MPa freezing pressure exhibited the highest average residual stress, reaching 3.5 MPa. Subsequently, the residual stress gradually decreased with increasing freezing pressure, declining to 0.85 MPa at 50 MPa, representing a reduction of 75.7%.

3.4. Tangent Modulus

Figure 7 presents the representative evolution curve of the tangent modulus with axial strain for the ice specimens subjected to various freezing pressures. The moving average method was applied to suppress inherent noise in the original data sequence. The evolution curve of the tangent modulus with axial strain can be divided into two distinct stages, with 2% axial strain serving as the transition point. In the initial fluctuating stage, the tangent modulus either increased sharply to a peak followed by a rapid decline or increased to a near-peak value followed by fluctuation before eventually stabilizing. When the axial strain exceeds 2%, the tangent modulus tends to stabilize stage. It is noteworthy that, despite variations in freezing pressure, all ice specimens converge to nearly identical tangent modulus values at an axial strain of 5%, fluctuating around zero within the range of 0 to 0.061 GPa.

Sun’s study revealed that the initial voids between ice crystals gradually diminish under loading, leading to enhanced interaction forces among ice microstructures [33]. This phenomenon manifests macroscopically as a progressive increase in the tangent modulus, representing the elastic deformation stage of ice. Once these initial voids are essentially closed, localized phenomena such as stress concentration, intracrystalline dislocation pile-up, and grain boundary sliding collectively induce irreversible deformation. Consequently, the ice can no longer sustain its original rate of stress increase, causing the tangent modulus to reach its peak value. This stage corresponds to the rapid strain-dependent increase in the tangent modulus prior to reaching its peak value. As a key parameter for characterizing the stiffness and deformation behavior of ice, the peak tangent modulus was extracted and is presented in Figure 8. The evolution curve exhibits a fluctuating trend with increasing freezing pressure. Specifically, the average peak tangent modulus values under freezing pressures of 10, 20, 30, 40, and 50 MPa were measured as 1.86, 2.22, 2.07, 2.37, and 1.76 GPa, respectively.

3.5. Macroscopic Deformation and Failure Characteristics

Figure 9 presents the deformation and failure patterns of the HPFI specimens upon reaching the residual strain under axial loading. Unlike conventional geomaterials that typically exhibit distinct diagonal shear cracks during failure [34,35], the damaged HPFI specimens demonstrated a unique failure mode characterized by deformation primarily concentrated in the upper portion of the specimens.

Under relatively low freezing pressures (10 and 20 MPa), distinct intercrossing cracks were visibly observed propagating from the top down through all the specimens, although the overall structural integrity was maintained (Figure 9a,b). The corresponding deviatoric stress–axial strain curves demonstrated ductile failure characteristics at the mechanical level. At a freezing pressure of 30 MPa, the post-failure ice specimens (Figure 9c) exhibited no visible longitudinal cracks on their surfaces and maintained high transparency, a marked contrast to the specimens deformed under lower freezing pressures. This phenomenon was also reported by Sun [32]. With the further increase in the freezing pressure to 40 and 50 MPa (Figure 9d,e), the damaged ice specimens showed gradually decreasing transparency due to the presence of internal microcracks. Notably, the density of these microcracks was significantly lower than that observed in the specimens frozen under 10 and 20 MPa. At these higher pressures, a distinct crack nucleation zone became apparent in the central region, from which the cracks propagated axially outward.

4. Conclusions

To investigate the mechanical properties of deep HPFI under in situ axial loading conditions, ice specimens were prepared at freezing pressures of 10, 20, 30, 40, and 50 MPa. During the testing process, the axial pressure was continuously increased while a constant confining pressure, equal to the freezing pressure, was maintained. The evolutions of key mechanical parameters, namely the peak deviatoric stress, residual deviatoric stress, and tangent modulus, during the deformation and failure process of the ice samples were observed and analyzed. The main conclusions of this study are as follows.

(1)

Under all freezing pressures, the deviatoric stress–axial strain curves followed a consistent pattern, and each curve exhibited a rapid yet smooth transition around the peak deviatoric stress point, manifests as ductile failure characteristics. The peak deviatoric stress initially increased with rising freezing pressure, reaching a maximum value of 8.61 MPa at a critical transition pressure of 20 MPa, beyond which it progressively decreased, eventually declining to a minimum of 1.66 MPa at 50 MPa. Notably, the axial strain corresponding to the peak deviatoric stress are all below 1%.

(2)

At 5% axial strain, all specimens formed under varying freezing pressures entered the residual stage, characterized by relatively stable stress levels. The residual deviatoric stress decreased significantly with increasing freezing pressure, declining from approximately 3.5 MPa at 10 MPa to 0.85 MPa at 50 MPa, corresponding to a total reduction of 75.7%. An axial strain of 2% marks the transition point at which the tangent modulus shifts from a fluctuating stage to a stable stage. The peak tangent modulus demonstrated a fluctuating trend with increasing freezing pressure, ranging from 1.76 to 2.37 GPa.

(3)

In these triaxial shear experiments, the deformed ice specimens did not exhibit the typical oblique fractures commonly observed in conventional geomaterials. Under freezing pressures of 10 and 20 MPa, the ice specimens developed interconnected crack networks upon failure. As the freezing pressure increased to 30 MPa, the failed ice specimens exhibited high transparency. When the pressure was further elevated to 40 and 50 MPa, the damaged specimens showed reduced transparency with limited microcracking, demonstrating significantly fewer cracks compared to the specimens frozen at 10 and 20 MPa.

This study set the experimental temperature of ice specimens at −10 °C, which falls within the typical range commonly used in laboratory experiments. However, significant differences exist between this condition and the actual ice-bearing environments encountered in practical engineering applications, such as deep artificial ground freezing and polar ice sheet drilling. As a result, the current experimental findings exhibit certain limitations in practical engineering applications. In subsequent phases of the HPFI research, we will expand the experimental temperature range to enhance the alignment and applicability of the results with field engineering conditions.